# General Discussion of Body Motion in an Ideal Infinite Fluid

• Alexandr I. Korotkin
Chapter
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 88)

The notion of added mass was first introduced by Dubua in 1776 (see [Birkhoff, G.: Hydrodynamics. Princeton Univ. Press, Princeton (1960)]), who experimentally studied the small oscillations of a spherical pendulum. An exact mathematical expression for the added mass of a sphere was obtained by Green in 1833 and Stokes in 1843 (see [Lamb, G.: Hydrodynamics. Cambridge University Press, Cambridge (1932)]). Stokes also studied the motion of a sphere in a finite volume of fluid. Later, as a result of efforts of many researchers, the notion of added mass was generalized to an arbitrary body moving in different regimes. Under motion of a body in real incompressible fluid, the hydrodynamic forces and torques are determined by inertial and viscous properties of the fluid. In certain approximations one can distinguish the forces and torques of inertial nature, which can be computed assuming that the fluid is ideal (non-viscous), and the forces (torques) are related to viscosity. The forces and torques of the inertial nature can be expressed in terms of the added masses of the body. The hydrodynamic forces and torques can also be expressed in terms of added masses not only in the case of accelerated motion, but also in the case of motion with constant velocity. It is especially important to take the added masses (or added moments of inertia) into account if they are comparable with the mass (or moments of inertia) of the body itself.

## Keywords

Body Motion Constant Velocity Hydrodynamic Force Transformation Formula Constant Angular Velocity
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